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1D Dirac Operators with Special Periodic Potentials

Djakov P., Mityagin B.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 1

59--75

For one-dimensional Dirac operators of the form [formula] we single out and study a class X of π-periodic potentials v whose smoothness is determined only by the rate of decay of the related spectral gaps γn=|λ+n−λ−n|, where λ±n are the eigenvalues of L=L(v) considered on [0,π] with periodic (for even n) or antiperiodic (for odd n) boundary conditions.